A new stable and more responsive solution for mcst problems

Minimum cost spanning tree (mcst) problems try to connect agents e¢ ciently to a source when agents are located at di¤erent points in space and the cost of using an edge is …xed. Two solution concepts to share the common cost of connection among users are based on the Shapley value: the Kar and the folk solutions. The Kar solution applies the Shapley value to the stand-alone cost game, which might be non-concave and non-monotonic, yielding cost allocations that might be unstable or negative. The folk solution modi…es the costs of some edges, yielding a monotonic and concave cost game, and thus non-negative allocations that are always in the core. We show necessary conditions for a mcst problem to generate a non-concave cost game. Using this result, we o¤er a new solution by modifying the cost of some edges, less than for the folk solution but enough to generate a concave but not necessarily monotonic cost game. Taking the Shapley value of this game gives allocations that are always in the core but possibly negative. It is also a compromise between the Kar and folk solutions as it satis…es more properties that make agents responsible for their locations in the network. We also examine more closely the incompatibilities between properties assuring stability and responsibility for one’s location, as well as the link between these properties and the non-negativity of the cost shares.